{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Testing the circular standard deviation for a uniform distribution of angles\n",
    "import numpy as np\n",
    "import FIELDMAPS_Plots as Fplot\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading catalogs\n",
      "Fil1/Fil1_CatO.txt\n",
      "Fil2/Fil2_CatO.txt\n",
      "Fil4/Fil4_CatO.txt\n",
      "Fil5/Fil5_CatO.txt\n",
      "Snake/Snake_CatO.txt\n",
      "Fil8/Fil8_CatO.txt\n",
      "Fil10/Fil10_CatO.txt\n",
      "G24/G24_CatO.txt\n",
      "G47/G47_CatO.txt\n",
      "G49/G49_CatO.txt\n",
      "Individual array shapes\n",
      "(5574,)\n",
      "(14459,)\n",
      "(10876,)\n",
      "(6266,)\n",
      "(6522,)\n",
      "(3367,)\n",
      "(8881,)\n",
      "(26222,)\n",
      "(9553,)\n",
      "(12824,)\n",
      "Shape of the final combined array\n",
      "(104544,)\n"
     ]
    }
   ],
   "source": [
    "# Listing all the filament names\n",
    "Names_List = ['Fil1', 'Fil2', 'Fil4', 'Fil5', 'Snake', 'Fil8', 'Fil10', 'G24', 'G47', 'G49']\n",
    "Labels_List = ['Fil1', 'Fil2', 'Fil4', 'Fil5', 'Fil6', 'Fil8', 'Fil10', 'G24', 'G47', 'G49']\n",
    "Labels_List2 = ['Fil 1', 'Fil 2', 'Fil 4', 'Fil 5', 'Fil 6', 'Fil 8', 'Fil 10', 'G24', 'G47', 'G49']\n",
    "# Creating list of arrays\n",
    "Bones_Catalogs = []\n",
    "print('Loading catalogs')\n",
    "# Loading the angle catalog for each bone\n",
    "for i in range (0, 10):\n",
    "    print(Names_List[i]+'/'+Names_List[i]+'_CatO.txt')\n",
    "    Catalog = np.loadtxt(Names_List[i]+'/'+Names_List[i]+'_CatO.txt')\n",
    "    Bones_Catalogs.append(Catalog)\n",
    "\n",
    "# Combining all the numpy arrays into one\n",
    "# Starting array for the iteration\n",
    "FullArray = Bones_Catalogs[0]\n",
    "print('Individual array shapes')\n",
    "print(np.shape(FullArray))\n",
    "# print(FullArray)\n",
    "# TestArray =  np.array(Bones_Catalogs[1])\n",
    "# print(np.shape(TestArray))\n",
    "# print(TestArray)\n",
    "# FullArray = np.concatenate((FullArray,Bones_Catalogs[1]))\n",
    "# print(np.shape(FullArray))\n",
    "for i in range (1, 10):\n",
    "    print(np.shape(Bones_Catalogs[i]))\n",
    "    FullArray = np.concatenate((FullArray,Bones_Catalogs[i]))\n",
    "print('Shape of the final combined array')\n",
    "print(np.shape(FullArray))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating mean and standard deviation of the catalog\n",
      "\n",
      "Mean: 6.807953675778338\n",
      "Standard deviation: 54.54414183045215\n",
      "\n",
      "Circular mean: 65.58840274130367\n",
      "Circular standard deviation: 56.58707286654089\n",
      "\n",
      "Number of bins: 36\n",
      "Bin size used: 5.0\n",
      "\n",
      "Using the circular mean to center the histogram\n",
      "Rolling histogram by -13 elements\n",
      "\n",
      "Fitting a Gaussian profile to the histogram\n",
      "\n",
      "Goodness of fit\n",
      "Number of iterations: 17\n",
      "Reduced chi-squared: 71101.46633535773\n",
      "\n",
      "Fitted parameters\n",
      "Amplitude:          3626.2823457088857\n",
      "                  ± 73.37395248351565\n",
      "\n",
      "Mean:               64.87159419465807\n",
      "                  ± 1.9424217177689622\n",
      "\n",
      "Standard deviation: 74.18030034114474\n",
      "                  ± 3.070111481913707\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of combined array from all bones\n",
    "HistoCombined = Fplot.Histogram(FullArray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rounding function to establish central bin\n",
    "def binround(x, base=5):\n",
    "    return base * math.floor(x/base) #round(x/base)\n",
    "\n",
    "# Shifting the range of angles for each catalog based on the previously calculated circular mean\n",
    "circ_mean = 65.58840274130367\n",
    "center_bin = binround(circ_mean)\n",
    "# Establishing the new limits\n",
    "minbin=center_bin-90.0\n",
    "maxbin=center_bin+90.0\n",
    "# Creating a copy of the catalogs\n",
    "Bones_Catalogs_P=Bones_Catalogs.copy()\n",
    "# Shifting the angles in each catalog\n",
    "for i in range(0,10):\n",
    "    # Checking size of catalog\n",
    "    IterArray = Bones_Catalogs_P[i]\n",
    "    size = np.shape(IterArray)\n",
    "    for j in range(0,size[0]):\n",
    "        if IterArray[j] < minbin:\n",
    "            IterArray[j] = IterArray[j]+180.0\n",
    "        if IterArray[j] > maxbin:\n",
    "            IterArray[j] = IterArray[j]-180.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x380 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a stacked histogram\n",
    "HistoStacked = plt.figure(figsize=(5.12,3.8))\n",
    "plt.hist(Bones_Catalogs_P, bins=36, stacked=True, label=Labels_List)#, range=(-90.0,90.0))\n",
    "#plt.xlim(-90.0, 90.0)\n",
    "plt.xlim(minbin, maxbin)\n",
    "axes = plt.gca() # Calling the axes object of the figure\n",
    "axes.xaxis.set_ticks_position('both') # Adding ticks to each side\n",
    "axes.yaxis.set_ticks_position('both') # Adding ticks to each side\n",
    "axes.legend(loc=(-0.1, 1.04), frameon=False,ncol=5) # loc=(1.04, 0),\n",
    "#plt.xticks(np.arange(-80.0, 90.0, 20.0))\n",
    "plt.xticks(np.arange(minbin+5, maxbin+1, 20.0))\n",
    "plt.axvline(x=circ_mean, color='black', linestyle='-', linewidth=2)\n",
    "plt.axvline(x=-180.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=-90.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=0.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=90.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=180.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.xlabel(r'Polarization Angle $\\theta$ (Degree)')\n",
    "plt.ylabel('Number')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Shifting the range of MAGNETIC FIELD angles for each catalog based on the previously calculated circular mean\n",
    "circ_mean = 65.58840274130367 + 90.0\n",
    "if circ_mean < -90.0:\n",
    "            circ_mean = circ_mean+180.0\n",
    "if circ_mean > 0.0:\n",
    "    circ_mean = circ_mean-180.0\n",
    "center_bin = binround(circ_mean)\n",
    "# Switching the polarization angles to magnetic field angles\n",
    "# Creating a copy of the catalogs\n",
    "Bones_Catalogs_B=Bones_Catalogs.copy()\n",
    "# Shifting the angles in each catalog\n",
    "for i in range(0,10):\n",
    "    # Checking size of catalog\n",
    "    IterArray = Bones_Catalogs_B[i] + 90.0\n",
    "    size = np.shape(IterArray)\n",
    "    for j in range(0,size[0]):\n",
    "        if IterArray[j] < -90.0:\n",
    "            IterArray[j] = IterArray[j]+180.0\n",
    "        if IterArray[j] > 90.0:\n",
    "            IterArray[j] = IterArray[j]-180.0\n",
    "    Bones_Catalogs_B[i] = IterArray # Replacing the list elements with the rotated arrays\n",
    "# Establishing the new limits\n",
    "minbin=center_bin-90.0\n",
    "maxbin=center_bin+90.0\n",
    "# Shifting the angles in each catalog\n",
    "for i in range(0,10):\n",
    "    # Checking size of catalog\n",
    "    IterArray = Bones_Catalogs_B[i]\n",
    "    size = np.shape(IterArray)\n",
    "    for j in range(0,size[0]):\n",
    "        if IterArray[j] < minbin:\n",
    "            IterArray[j] = IterArray[j]+180.0\n",
    "        if IterArray[j] > maxbin:\n",
    "            IterArray[j] = IterArray[j]-180.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x380 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a stacked histogram of MAGNETIC FIELD angles\n",
    "HistoStacked2 = plt.figure(figsize=(5.12,3.8))\n",
    "plt.hist(Bones_Catalogs_B, bins=36, stacked=True, label=Labels_List)#, range=(-90.0,90.0))\n",
    "#plt.xlim(-90.0, 90.0)\n",
    "plt.xlim(minbin, maxbin)\n",
    "axes = plt.gca() # Calling the axes object of the figure\n",
    "axes.xaxis.set_ticks_position('both') # Adding ticks to each side\n",
    "axes.yaxis.set_ticks_position('both') # Adding ticks to each side\n",
    "axes.legend(loc=(-0.1, 1.04), frameon=False,ncol=5) # loc=(1.04, 0),\n",
    "#plt.xticks(np.arange(-80.0, 90.0, 20.0))\n",
    "plt.xticks(np.arange(minbin+15, maxbin+1, 20.0))\n",
    "plt.axvline(x=circ_mean, color='black', linestyle='-', linewidth=2)\n",
    "plt.axvline(x=-180.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=-90.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=0.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=90.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.axvline(x=180.0, color='black', linestyle='--', linewidth=2)\n",
    "plt.xlabel(r'Magnetic Field Angle $\\theta_B$ (Degree)')\n",
    "plt.ylabel('Number')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-90.         -89.9999     -89.9998     ...  90.00070001  90.00080001\n",
      "  90.00090001]\n",
      "Calculating mean and standard deviation of the catalog\n",
      "\n",
      "Mean: 0.0004500029878045177\n",
      "Standard deviation: 51.96181290391786\n",
      "\n",
      "Circular mean: -89.9995499977051\n",
      "Circular standard deviation: 140.93312818780385\n",
      "\n",
      "Number of bins: 36\n",
      "Bin size used: 5.0\n",
      "\n",
      "Using the circular mean to center the histogram\n",
      "Rolling histogram by 18 elements\n",
      "\n",
      "Fitting a Gaussian profile to the histogram\n",
      "\n",
      "Goodness of fit\n",
      "Number of iterations: 180\n",
      "Reduced chi-squared: 1.7557046737131102e-10\n",
      "\n",
      "Fitted parameters\n",
      "Amplitude:          50000.000014212965\n",
      "                  ± 2.3798242519981644e-06\n",
      "\n",
      "Mean:               -90.00206302761767\n",
      "                  ± 1.4762786910960022\n",
      "\n",
      "Standard deviation: 2179412.001219427\n",
      "                  ± 43147.55074540604\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Testing the standard deviation for a flat distribution\n",
    "\n",
    "# Creating catalog of angles by steps of 0.1 degrees\n",
    "NumberAngles = 180.0*10.0\n",
    "FlatAnglesCatalog = np.arange(-90.0, 90.001, 0.0001)\n",
    "print(FlatAnglesCatalog)\n",
    "# Flat histogram of angles\n",
    "HistoFlat = Fplot.Histogram(FlatAnglesCatalog)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Saving the figures\n",
    "# PNG\n",
    "HistoStacked.savefig('All/Histogram_Stacked.png',dpi=300)\n",
    "HistoStacked2.savefig('All/Histogram_Stacked_B.png',dpi=300)\n",
    "HistoCombined[0].savefig('All/Histogram_Combined.png',dpi=300)\n",
    "# PDF\n",
    "HistoStacked.savefig('All/Histogram_Stacked.pdf',dpi=300)\n",
    "HistoStacked2.savefig('All/Histogram_Stacked_B.pdf',dpi=300)\n",
    "HistoCombined[0].savefig('All/Histogram_Combined.pdf',dpi=300)"
   ]
  }
 ],
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